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A249159 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

%I A249159 #6 Oct 28 2014 00:11:34
%S A249159 1,1,1,3,2,2,4,7,2,2,15,18,24,4,4,24,57,30,36,4,4,105,174,282,88,100,
%T A249159 8,8,192,561,414,570,120,132,8,8,945,1950,3660,1620,2040,312,336,16,
%U A249159 16,1920,6555,6090,9360,2820,3360,392,416,16,16,10395,25290,53370
%N A249159 Triangular array:  row n gives the coefficients of the polynomial p(n,x) defined in Comments.
%C A249159 The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = 1 + n)/(2*f(n-1,x)), where f(0,x) = 1.
%C A249159 (Sum of numbers in row n) = A000982(n+1) for n >= 0.
%C A249159 Column 1 is essentially A081405.
%H A249159 Clark Kimberling, <a href="/A249159/b249159.txt">Rows 0..100, flattened</a>
%F A249159 f(0,x) = 1/1, so that p(0,x) = 1
%F A249159 f(1,x) = (1 + x)/1, so that p(1,x) = 1 + x;
%F A249159 f(2,x) = (3 + 2 x + x^2)/(1 + x), so that p(2,x) = 3 + 2 x + x^2.
%F A249159 First 6 rows of the triangle of coefficients:
%F A249159 1
%F A249159 1    1
%F A249159 3    2     2
%F A249159 4    7     2     2
%F A249159 15   18    24    4     4
%F A249159 24   57    30    36    4    4
%t A249159 z = 15; f[x_, n_] := 1 + n/(2 f[x, n - 1]); f[x_, 1] = 1;
%t A249159 t = Table[Factor[f[x, n]], {n, 1, z}]
%t A249159 u = Numerator[t]
%t A249159 TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249159 array *)
%t A249159 Flatten[CoefficientList[u, x]] (* A249159 sequence *)
%Y A249159 Cf. A000982, A081405.
%K A249159 nonn,tabl,easy
%O A249159 0,4
%A A249159 _Clark Kimberling_, Oct 23 2014